一、兩種算子

一階導數—Sobel算子

水平梯度：

垂直梯度：

最終圖像梯度：

二階導數—Laplacian算子

在二階導數的時候，最大變化處的值為零，即邊緣是零值。
常見的拉普拉斯算子：、其所有元素之和為零。

二、Sobel算子

cv2.Sobel(image,cv2.CV_32F,1,0)image為代求的圖像；CV_32F為圖像的深度(32為float類型)，255肯定不夠，故選擇大點
cv2.convertScaleAbs(grad_x)將計算出來的正負數全部轉換為正值，然后轉換到8位的圖像上去

import cv2
import numpy as np
from matplotlib import pyplot as pltdef sobel(image):grad_x = cv2.Sobel(image,cv2.CV_32F,1,0)grad_y = cv2.Sobel(image,cv2.CV_32F,0,1)gradx = cv2.convertScaleAbs(grad_x)grady = cv2.convertScaleAbs(grad_y)cv2.imshow("gradient-x",gradx)cv2.imshow("gradient-y",grady)gradxy = cv2.addWeighted(gradx,0.5,grady,0.5,0)cv2.imshow("gradient",gradxy)src = cv2.imread(r"G:\Juptyer_workspace\study\opencv\opencv3\a1.jpg")
cv2.imshow("image",src)
cv2.namedWindow("image",cv2.WINDOW_AUTOSIZE)
sobel(src)cv2.waitKey(0)
cv2.destroyAllWindows()

效果圖如下：

三、Scharr算子(Sobel算子的增強版)，但對噪聲更加敏感

import cv2
import numpy as np
from matplotlib import pyplot as pltdef sobel(image):grad_x = cv2.Scharr(image,cv2.CV_32F,1,0)grad_y = cv2.Scharr(image,cv2.CV_32F,0,1)gradx = cv2.convertScaleAbs(grad_x)grady = cv2.convertScaleAbs(grad_y)cv2.imshow("gradient-x",gradx)cv2.imshow("gradient-y",grady)gradxy = cv2.addWeighted(gradx,0.5,grady,0.5,0)cv2.imshow("gradient",gradxy)src = cv2.imread(r"G:\Juptyer_workspace\study\opencv\opencv3\a1.jpg")
cv2.imshow("image",src)
cv2.namedWindow("image",cv2.WINDOW_AUTOSIZE)
sobel(src)cv2.waitKey(0)
cv2.destroyAllWindows()

效果圖如下：

四、Laplacian算子(直接調用API)

import cv2
import numpy as np
from matplotlib import pyplot as pltdef lapalian(image):dst = cv2.Laplacian(image,cv2.CV_32F)lpls = cv2.convertScaleAbs(dst)cv2.imshow("lapalian",lpls)src = cv2.imread(r"G:\Juptyer_workspace\study\opencv\opencv3\a1.jpg")
cv2.imshow("image",src)
cv2.namedWindow("image",cv2.WINDOW_AUTOSIZE)
lapalian(src)cv2.waitKey(0)
cv2.destroyAllWindows()

效果圖如下：

五、Laplacian算子(自定義卷積核)

import cv2
import numpy as np
from matplotlib import pyplot as pltdef lapalian(image):#kernel = np.array([[1,1,1],[1,-8,1],[1,1,1]])kernel = np.array([[0,1,0],[1,-4,1],[0,1,0]])dst = cv2.filter2D(image,cv2.CV_32F,kernel=kernel)lpls = cv2.convertScaleAbs(dst)cv2.imshow("lapalian",lpls)src = cv2.imread(r"G:\Juptyer_workspace\study\opencv\opencv3\a1.jpg")
cv2.imshow("image",src)
cv2.namedWindow("image",cv2.WINDOW_AUTOSIZE)
lapalian(src)cv2.waitKey(0)
cv2.destroyAllWindows()

效果圖如下：